UDC 519.6
MATHEMATICAL MODELING OF SPATIALLY DISTRIBUTED SYSTEMS, POLYNOMIALLY
DEPENDENT ON LINEAR DIFFERENTIAL TRANSFORMATIONS OF THE STATE FUNCTION
Abstract. Initial–boundary-value problems of the dynamics of nonlinear spatially distributed systems are formulates and solved according to the root-mean-square criterion. Systems whose linear mathematical model is supplemented by the polynomially defined dependence on the differential transformation of their state function are considered. Analytical dependences of this function are generated under the presence of their discretely and continuously defined initialboundary-value observations, without constraints on the number and quality of the latter. The accuracy of the sets of the obtained solutions is evaluated, and their uniqueness is analyzed.
Keywords: nonlinear dynamical systems, systems with uncertainties, distributed-parameter systems, spatially distributed systems, pseudosolutions, ill-posed initial–boundary-value problems.
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